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Polariton spin transport in a microcavity channel:A mean-field modelingM.Yu.Petrov1 and A.V.Kavokin1,21Spin Optics Laborato...
Outline• Motivation for experimentalists• Mean-field model and its numerical implementation• Results of modeling   • Interf...
Motivation for experimentalists           pump-L                 pump-R                                       Quantum Well...
Mean-field model                                           ↵2 =    0.1↵18                    ⇣    2                        ...
Numerical implementation• Spatial discretization by using Finite Element Method   • Quadratic elements   • Grid size: ∆x<0...
Interference of two pump pulses
Interference of two pump pulses (2)current density                iù     ⇤              ⇤           j=      (   ±r   ±   ±...
Interference of two pump pulses (2)current density                iù     ⇤              ⇤           j=      (   ±r   ±   ±...
Spin-polarized polariton transport
Spin-polarized polariton transport
Spin-polarized polariton transport           2         2     |   +|      |   |⇢c =     |   + |2   +|   |2
Conductivity tensor        @                  ⇣   ù2 2                                            iù ⌘                    ...
Spin-current density with diferent pump-pulses             h           ù n+ r+ i ⇣             ⌘h    +    +   i           ...
Summary and further steps• A mean-field model describing polariton spin transport based on coupled  Gross-Pitaevskii equati...
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17.04.2012 m.petrov

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17.04.2012 m.petrov

  1. 1. Polariton spin transport in a microcavity channel:A mean-field modelingM.Yu.Petrov1 and A.V.Kavokin1,21Spin Optics Laboratory, Saint Petersburg State University, Russia2Physics and Astronomy School, University of Southampton, UK SOLAB seminar, Apr. 17, 2012
  2. 2. Outline• Motivation for experimentalists• Mean-field model and its numerical implementation• Results of modeling • Interference of two flows in a channel • Spin-polarized polariton transport in a channel • Interpretation in terms of spin conductivity• Summary and further steps
  3. 3. Motivation for experimentalists pump-L pump-R Quantum Well Bragg Mirrors
  4. 4. Mean-field model ↵2 = 0.1↵18 ⇣ 2 ⌘<iù @ ù iù @t + (x, t) = r2 + ↵1 | 2 + (x, t)| + ↵2 | (x, t)|2 + (x, t) + p+ (x, t) ⇣ 2m 2⌧ ⌘:iù @ ù2 iù @t (x, t) = 2m r2 + ↵1 | (x, t)|2 + ↵2 | + (x, t)| 2 2⌧ (x, t) + p (x, t) ⌧ 10ps 5 m 3 ⇥ 10 m0 (x xL )2 L p± (x, t) =p± e x2 eiwL t+ikL ·x + (x xR )2 R p± e x2 eiwR t+ikR ·x
  5. 5. Numerical implementation• Spatial discretization by using Finite Element Method • Quadratic elements • Grid size: ∆x<0.25µm @ Lch~100µm• Time discretization u0 = f (t, u), u(t0 ) = u0 ; • 5-step Backward Differentiation Formula s X ak un+k = h f (tn+s , un+s ); k=1 • Max time step: ∆t<100fs @ τ=10ps tn = t0 + nh.• Implementation using Comsol (2D and 1D) and a private software (1D)
  6. 6. Interference of two pump pulses
  7. 7. Interference of two pump pulses (2)current density iù ⇤ ⇤ j= ( ±r ± ±r ±) 2m
  8. 8. Interference of two pump pulses (2)current density iù ⇤ ⇤ j= ( ±r ± ±r ±) 2m
  9. 9. Spin-polarized polariton transport
  10. 10. Spin-polarized polariton transport
  11. 11. Spin-polarized polariton transport 2 2 | +| | |⇢c = | + |2 +| |2
  12. 12. Conductivity tensor @ ⇣ ù2 2 iù ⌘ 2 2 iù ± = r + ↵1 | ±| + ↵2 | ⌥| ± + P± @t 2m 2⌧ p ± = n± ei± @n± Imaginary part of GP eq. decomposition gives: + div j = 0 @t ù h n+ r+ i ⇣ ⌘h + + µR µL i j= n r = ++ + µR µL m + (x x0 )2 ± (x, t) = ± (x)e iµ± t/ù P± = p0 e 2 ei!± t/ù+ik± ·x ⇣ ù2 2 iù ⌘ 2 2 0 µ± ± (x) = r + ↵1 | ±| + ↵2 | ⌥| ± (x) + P± (x) 2m 2⌧
  13. 13. Spin-current density with diferent pump-pulses h ù n+ r+ i ⇣ ⌘h + + i µR µL j= n r = ++ + µR µL m +
  14. 14. Summary and further steps• A mean-field model describing polariton spin transport based on coupled Gross-Pitaevskii equations is developed • Numerical implementation of the model demonstrates interference of two flows stimulated by CW excitation near both boundaries of a channel • If pumps are cross-polarized the effect can be emphasized by detection of circular polarization degree• Further steps • Possibility of experimental observation

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